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Let \(f=a/b\in F(z)\)  be such that \(a, b\in F[z]\)  and \(\gcd (a, b)=1\) . Then \(f\)  is \(\tau _{q, z}\) -summable in \(F(z)\)  if and only if \({\operatorname{res}}_{\tau _{q, z}}(f, \infty ) =0\)  and
\({\operatorname{res}}_{\tau _{q, z}}(f, d, j)=0\)  for any irreducible factor \(d\)  of the denominator \(b\)  of any multiplicity \(j\in  {\mathbb {N}}\) .
